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He says it because it's pretty much true at that point in the timeline, in that they are shadows of their former selves, nowhere near the size and scope they both once held.

S.H.I.E.L.D. is pretty much in disarray after the events of The Winter Soldier, in which we learn Hydra agents were able to infiltrate the agency in an effort to use their resources to finally push humanity into giving up their freedom, which Hydra learned years ago they couldn't force. While the mid-credits scene seems to show Hydra still exists, they're seemingly operating on a much smaller and possibly more focused basis.

As such, saying they don't exist anymore could be taken to mean they don't exist at a level that they matter or are viable options to work with anymore. Burch is a big arms dealer, so if they're not able to come through financially the way the once did, and thus in his mind they simply don't exist and aren't worth bothering with.